Question: The sum of two numbers is $111$, and their difference is $81$. What are the two numbers?
Explanation: Let $x$ be the first number, and let $y$ be the second number. The system of equations is: ${x+y = 111}$ ${x-y = 81}$ Solve for $x$ and $y$ using elimination. Add the top and bottom equations together. $ 2x = 192 $ $ x = \dfrac{192}{2} $ ${x = 96}$ Now that you know ${x = 96}$ , plug it back into $ {x+y = 111}$ to find $y$ ${(96)}{ + y = 111}$ ${y = 15}$ You can also plug ${x = 96}$ into $ {x-y = 81}$ and get the same answer for $y$ ${(96)}{ - y = 81}$ ${y = 15}$ Therefore, the larger number is $96$, and the smaller number is $15$.